Two things that make me think this isn’t a Pacific Northwest language:

1) None of the long sequences of consonants without vowels that are such a typical areal feature.
2) Nasal vowels [î] and [ã], which as far as I know (though I may be mistaken here) don’t occur in Pacific Northwest languages. They do appear in Siouan languages, like Lakhota.

Add to this what sounds like high tones and I would be sorely tempted to think this might be Lakhota — except that as far as I know, Lakhota doesn’t have voiceless lateral fricatives, which abound in this recording. Hmm.

Perhaps Tlingit, as Chris Sundita suggested, or Kwakwala? I’m still not sure because of those nasal vowels…